Finite Group Databasebeta

← #34047389

Subgroups — #34047389

Order 19072.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011883C211yesmaximal, characteristic
2C2×C4×C22⋊D149C211yesmaximal, characteristic, complemented
3#23749516C211yesmaximal, characteristic, complemented
4#23749513C211yesmaximal, characteristic, complemented
5#23749509C211yesmaximal, characteristic, complemented
6#23749506C211yesmaximal, characteristic, complemented
7#23749505C211yesmaximal, characteristic, complemented
8#23749504C211yesmaximal, characteristic, complemented
9#23749502C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic, complemented
11#23749498C211yesmaximal, characteristic, complemented
12#23749496C211yesmaximal, characteristic, complemented
13#23749483C211yesmaximal, characteristic, complemented
14C2×#18011818C211yesmaximal, characteristic, complemented
15C2×C4×D4×C149C211yesmaximal, characteristic, complemented
16C22×C22⋊D149C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C23×Dic149C2211yescharacteristic
19C23×Dic149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21#18011883C418yescomplemented
22C4×C22⋊D149—24no—
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×C22⋊Dic149C2211yescharacteristic
29C2×C22⋊Dic149C2211yescharacteristic
30C2×C22⋊Dic149C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36#18011818C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45#18011818C2211yescharacteristic
46C22×D4×C149C2211yescharacteristic
47C23×C4×C149C2211yescharacteristic
48C23×C4×C149C2211yescharacteristic
49C4×D4×C149—24no—
50C2×C4⋊C4×C149C2211yescharacteristic
51C2×C22⋊C4×C149C2211yescharacteristic
52C2×C22⋊C4×C149C2211yescharacteristic
53C2×C42×C149C2211yescharacteristic
54C23×D149C2311yescharacteristic
55C2×C22⋊D149—22no—
56C2×C22⋊D149—22no—
57C2×C22⋊D149—41no—
58C2×C22⋊D149—41no—
59C2×C22⋊D149C2×C414yescomplemented
60C2×C22⋊D149C2×C414yescomplemented
61C22×Dic149—22no—
62C22×Dic149—41no—
63C22×Dic149—41no—
64C22×Dic149—41no—
65C22×Dic149—41no—
66C22×Dic149C2×C414yescomplemented
67C22×Dic149C2311yescharacteristic
68C22×Dic149C2311yescharacteristic
69C22×Dic149C2311yescharacteristic
70C22×Dic149C2311yescharacteristic
71C22×Dic149C2311yescharacteristic
72C22×Dic149C2311yescharacteristic
73C22×Dic149C2311yescharacteristic
74C2×C4×D149—22no—
75C2×C4×D149—41no—
76C2×C4×D149—41no—
77#14558715—22no—
78#14558715—41no—
79#14558715—41no—
80#14558715C2×C414yescomplemented
81C22⋊Dic149—22no—
82C22⋊Dic149—41no—
83C22⋊Dic149—41no—
84C22⋊Dic149C2×C414yescomplemented
85#14558713—22no—
86#14558713—41no—
87#14558713—41no—
88#14558713C2×C414yescomplemented
89C4×Dic149—22no—
90C24×C149C2311yescharacteristic
91C24×C149C2311yescharacteristic
92C2×D4×C149—22no—
93C2×D4×C149—22no—
94C2×D4×C149C2×C414yescomplemented
95C22×C4×C149—22no—
96C22×C4×C149—41no—
97C22×C4×C149—41no—
98C22×C4×C149—41no—
99C22×C4×C149—41no—
100C22×C4×C149D414yescomplemented
101C22×C4×C149C2311yescharacteristic
102C22×C4×C149C2311yescharacteristic
103C22×C4×C149C2311yescharacteristic
104C22×C4×C149C2311yescharacteristic
105C22×C4×C149C2311yescharacteristic
106C4⋊C4×C149—22no—
107C22⋊C4×C149—22no—
108C22⋊C4×C149—22no—
109C42×C149—22no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149C22×C412yes—
117C22⋊D149—28no—
118C22⋊D149—44no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—44no—
138C2×Dic149—44no—
139C2×Dic149C22×C412yes—
140C2×Dic149C22×C412yes—
141C2×Dic149C22×C412yes—
142C4×D149—44no—
143C23×C149—21no—
144C23×C149—21no—
145C23×C149—21no—
146C23×C149—21no—
147C23×C149—21no—
148C23×C149—21no—
149C23×C149—21no—
150C23×C149—21no—
151C23×C149—21no—
152C23×C149—21no—
153C23×C149C22×C412yes—
154C23×C149C22×C412yes—
155C23×C149C2×D412yes—
156C23×C149#4112yes—
157C23×C149C2411yescharacteristic
158D4×C149—28no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149—21no—
167C2×C4×C149—21no—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—21no—
171C2×C4×C149—44no—
172C2×C4×C149—44no—
173C2×C4×C149C22×C412yes—
174C2×C4×C149C2×D412yes—
175C2×C4×C149C2×D412yes—
176C22×C149—22no—
177C22×C149—22no—
178C22×C149—22no—
179C22×C149—22no—
180C22×C149—22no—
181C22×C149—22no—
182C22×C149—22no—
183C22×C149—22no—
184C22×C149—22no—
185C22×C149—41no—
186C22×C149—41no—
187C22×C149—41no—
188C22×C149—41no—
189C22×C149C4×D414yes—
190C22×C149C23×C411yescharacteristic
191C22×C149C22×D411yescharacteristic
192C22×C149C2×#4111yescharacteristic
193C22×C149H(5,𝔽2)11yescharacteristic
194C22×C149H(5,𝔽2)11yescharacteristic
195C22×C149H(5,𝔽2)11yescharacteristic
196C22×C1492−1+411yescharacteristic
197C2×D149—22no—
198C2×D149—22no—
199C2×D149—22no—
200C2×D149—41no—
201C2×D149—41no—
202C2×D149—41no—
203C2×D149—41no—
204C4×C149—22no—
205C4×C149—22no—
206C4×C149—22no—
207C4×C149—41no—
208C4×C149—41no—
209Dic149—22no—
210Dic149—22no—
211Dic149—22no—
212Dic149—41no—
213Dic149—41no—
214Dic149—41no—
215Dic149—41no—
216C2×C149—24no—
217C2×C149—42no—
218C2×C149C2×C4×D411yescharacteristic
219C2×C149#51811yescharacteristic
220C2×C149#52011yescharacteristic
221C2×C149#53411yescharacteristic
222C2×C149#53711yescharacteristic
223C2×C149#53811yescharacteristic
224C2×C149#53911yescharacteristic
225D149—42no—
226C149#232511yescharacteristic, complemented, Sylow
227#2325—1491nomaximal, Sylow
228C2×#121—1491no—
229C2×C4×D4—1491no—
230C2×C4×D4D14911yescharacteristic, complemented
231#388—1491no—
232#388—1491no—
233#387—1491no—
234#387—1491no—
235#386—1491no—
236#386—1491no—
237#386—1491no—
238#386—1491no—
239#385—1491no—
240#385—1491no—
241#380—1491no—
242C2×#95—1491no—
243C22×D4—1491no—
244C22×D4—1491no—
245C22×D4C2×D14911yescharacteristic
246C23×C4—1491no—
247C23×C4—1491no—
248C23×C4—1491no—
249C23×C4C2×D14911yescharacteristic
250C23×C4C2×D14911yescharacteristic
251#121—1498no—
252C4×D4—24no—
253C4×D4—2984no—
254C2×C4⋊C4—1491no—
255C2×C4⋊C4—1491no—
256C2×C4⋊C4—1491no—
257C2×C4⋊C4—1491no—
258C2×C4⋊C4C2×D14911yescharacteristic
259C2×C22⋊C4—1491no—
260C2×C22⋊C4—1491no—
261C2×C22⋊C4—1491no—
262C2×C22⋊C4—1491no—
263C2×C22⋊C4—1491no—
264C2×C22⋊C4—1491no—
265C2×C22⋊C4—1491no—
266C2×C22⋊C4—1491no—
267C2×C22⋊C4C2×D14911yescharacteristic
268C2×C22⋊C4C2×D14911yescharacteristic
269C2×C42—1491no—
270C2×C42C2×D14911yescharacteristic
271#95—1491no—
272#95—1491no—
273#95—1491no—
274#95—1491no—
275#95—1491no—
276#95—1491no—
277#95—1491no—
278#95—1491no—
279#95—1491no—
280#95—1491no—
281C24—1491no—
282C24C22×D14911yescharacteristic
283C24C22×D14911yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—2982no—
287C2×D4—2982no—
288C2×D4—5961no—
289C2×D4—5961no—
290C2×D4—1494no—
291C2×D4—1494no—
292C2×D4C4×D14914yescomplemented
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—2982no—
299C22×C4—2982no—
300C22×C4—5961no—
301C22×C4—5961no—
302C22×C4—5961no—
303C22×C4—5961no—
304C22×C4—5961no—
305C22×C4—5961no—
306C22×C4—1491no—
307C22×C4—1491no—
308C22×C4—1491no—
309C22×C4—1491no—
310C22×C4—1491no—
311C22×C4—1491no—
312C22×C4—1491no—
313C22×C4—1494no—
314C22×C4C22⋊D14914yescomplemented
315C22×C4C22×D14911yescharacteristic
316C22×C4C22×D14911yescharacteristic
317C22×C4C22×D14911yescharacteristic
318C22×C4C22×D14911yescharacteristic
319C22×C4C22×D14911yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—2982no—
322C4⋊C4—5961no—
323C4⋊C4—5961no—
324C4⋊C4—1494no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—2982no—
328C22⋊C4—2982no—
329C22⋊C4—5961no—
330C22⋊C4—5961no—
331C22⋊C4—5961no—
332C22⋊C4—5961no—
333C22⋊C4—1494no—
334C22⋊C4—1494no—
335C42—22no—
336C42—2982no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—2981no—
348C23—2981no—
349C23—2981no—
350C23—2981no—
351C23—2981no—
352C23—2981no—
353C23—1492no—
354C23C2×C4×D14912yes—
355C23C2×C4×D14912yes—
356C23C2×C22⋊D14912yes—
357C23#1455873612yes—
358C23C23×D14911yescharacteristic
359D4—28no—
360D4—2988no—
361D4—5964no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—2981no—
377C2×C4—2981no—
378C2×C4—2981no—
379C2×C4—2981no—
380C2×C4—2981no—
381C2×C4—2981no—
382C2×C4—2981no—
383C2×C4—2981no—
384C2×C4—2981no—
385C2×C4—2981no—
386C2×C4—2981no—
387C2×C4—2981no—
388C2×C4—2981no—
389C2×C4—2981no—
390C2×C4—2981no—
391C2×C4—2981no—
392C2×C4—2981no—
393C2×C4—2981no—
394C2×C4—5964no—
395C2×C4—5964no—
396C2×C4—5964no—
397C2×C4—1492no—
398C2×C4—1492no—
399C2×C4—1492no—
400C2×C4C2×C4×D14912yes—
401C2×C4C2×C22⋊D14912yes—
402C2×C4C2×C22⋊D14912yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—2982no—
417C22—2982no—
418C22—2982no—
419C22—5961no—
420C22—5961no—
421C22—5961no—
422C22—5961no—
423C22C4×C22⋊D14914yes—
424C22C22×C4×D14911yescharacteristic
425C22C22×C22⋊D14911yescharacteristic
426C22C2×#1455873611yescharacteristic
427C22#1801195611yescharacteristic
428C22#1801195611yescharacteristic
429C22#1801195711yescharacteristic
430C22#1801195811yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—2982no—
437C4—2982no—
438C4—2982no—
439C4—5961no—
440C4—5961no—
441C4—5961no—
442C4—5961no—
443C2—24no—
444C2—42no—
445C2—5962no—
446C2C2×C4×C22⋊D14911yescharacteristic
447C2#2375009711yescharacteristic
448C2#2375010411yescharacteristic
449C2#2375018411yescharacteristic
450C2#2375020311yescharacteristic
451C2#2375020811yescharacteristic
452C2#2375021711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC2×C4×D4×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011883C2
hypercenterC2×C4×D4D149
hypocenterC149#2325
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×C22⋊D149C2semidirect
3. #23749516C2semidirect
4. #23749513C2semidirect
5. #23749509C2semidirect
6. #23749506C2semidirect
7. #23749505C2semidirect
8. #23749504C2semidirect
9. #23749502C2semidirect
10. #23749501C2semidirect
11. #23749498C2semidirect
12. #23749496C2semidirect
13. #23749483C2semidirect
14. C2×#18011818C2semidirect
15. C2×C4×D4×C149C2semidirect
21. #18011883C4semidirect
59. C2×C22⋊D149C2×C4semidirect
60. C2×C22⋊D149C2×C4semidirect
66. C22×Dic149C2×C4semidirect
80. #14558715C2×C4semidirect
84. C22⋊Dic149C2×C4semidirect
88. #14558713C2×C4semidirect
94. C2×D4×C149C2×C4semidirect
100. C22×C4×C149D4semidirect
226. C149#2325semidirect
230. C2×C4×D4D149semidirect
292. C2×D4C4×D149semidirect
314. C22×C4C22⋊D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180118832
C2×C4×C22⋊D1492
#237495162
#237495132
#237495092
#237495062
#237495052
#237495042
#237495022
#237495012
#237494982
#237494962
#237494832
C2×#180118182
C2×C4×D4×C1492
#2325149